An absorption spectroscopy instrument is provided with a re-injection mirror to greatly increase the optical power coupled into an optical cavity, comprised of two or more mirrors, for the purpose of increasing the quality of absorption and extinction measurements made in the cavity. Light reflected from the first cavity mirror upon which a light beam is incident, can be efficiently collected and back reflected onto the same mirror, effectively producing a plurality of optical injections into the cavity. The instrument can be used for off-axis cavity ringdown spectroscopy, off-axis integrated cavity output spectroscopy, or other cavity-based spectroscopy applications.